Indefinite Integrals: An Exploration 🌿

Understanding the Basics

Indefinite integrals, often referred to as antiderivatives, are functions that reverse the process of differentiation. They are fundamental in finding solutions to differential equations.

Consider the function f(x) = x^2. Its indefinite integral is represented as /text int f(x) \\, dx = F(x) + C/ where F(x) = (1/3)x^3 and C is the constant of integration.

Exploring Properties

• Linearity: ∫[af(x) + bg(x)]dx = a∫f(x)dx + b∫g(x)dx
• Power Rule: ∫x^n dx = (x^(n+1))/(n+1) + C, n ≠ -1
• Constant Rule: ∫c dx = cx + C